数字图像去噪算法研究及应用
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摘要
数字图像的噪声主要来源于图像采集和传输的过程,是干扰图像质量最主要的因素之一,同时还影响着人们对图像信息的读取以及对图像所做的后续处理,所以图像去噪问题一直是数字图像研究领域中的一个研究热点。本文对图像去噪的一些关键技术和算法进行了较为深入的探索和研究,所做的主要工作如下:
首先介绍了数字图像去噪算法的发展概况和研究现状,在总结一些传统去噪算法的同时指出了去噪算法中几个最新的研究领域;然后提出了几种常见图像噪声的数学统计模型和去噪质量评判标准,接着介绍了两大传统图像去噪算法:中值滤波法和维纳滤波法,对它们的去噪原理和性能进行了详细的讨论与分析。
其次研究了两种最新的图像分析工具:小波变换和多尺度几何变换理论,重点探讨如何将小波变换和Contourlet变换应用于图像去噪,分析了图像经过这两种变换后系数的分布特点以及阈值函数的选取原理,并在此基础上提出了一种基于Contourlet变换的分层阈值去噪算法;并且对以上算法进行了详细的仿真实验,分析了它们的去噪性能。
最后针对原Contourlet变换中的缺陷,提出了一种改进的非采样Contourlet变换:多小波—非采样Contourlet变换:首先利用多小波对图像进行多尺度分解,再结合非下采样方向滤波器组进行方向分解。并将此变换应用于图像去噪之中,并根据分解所得到的各方向子带的关系,改进了Bayes Shrink自适应阈值取值方法,由此提出了一种基于多小波—非采样Contourlet变换的自适应阈值去噪算法。本文对该算法进行仿真实验,且与一些已有的去噪算法进行了对比,实验结果表明:应用此算法的图像去噪效果与传统算法相比,有了一定的提高,能够保留更多的图像细节信息,且具有一定的实用价值。
Digital image noise mainly originates from the process of image acquisition and transmission, which also is one of the main factors influencing the quality of image information. Therefore image de-noising is a popular research subject in image processing area. This paper has researched some crucial techniques and algorisms deeply on this area. The main work and research results will be given as follows:
Firstly this paper provides an overview of development and current situation on image de-noising, and proposes some latest research area, gives some common image statistical mathematical model and the standard of judgment of de-noising quality, then introduces two classical de-noising algorithms :media filter method and wiener filter method, analyses and discusses their de-noising principles and properties emphatically.
Secondly this paper discusses two latest image analysis tools: wavelet transform and Multi-scale Geometry transform, discusses how to apply this two transform on image de-noising, analyses their spreading property of coefficients and threshold choosing principles; on this basic this paper proposes a hierarchical threshold de-noising method based on Contourlet transform, carries on simulation experiment to these algorithm and compares their de-noising results.
Finally according to the drawbacks of Contourlet transform, this paper proposes an improved Contourlet transform: multi wavelet-nonsubsampled Contourlet transform, this algorithm uses multi wavelet for multi-scale decomposing and combines nonsubsampled filter banks for multi-direction decomposing, applies this transform on image de-noising and improves Bayes Shrink Adaptive Threshold method according to the relation between the decomposing sub bands. So this paper proposes a new algorithm which is called multi wavelet-nonsubsampled Contourlet transform de-noising algorithm. The experiment result shows this algorithm is superior to some traditional algorithm that can reserve more image detail information and get a better de-noising effect, which also has certain of application value.
首先介绍了数字图像去噪算法的发展概况和研究现状,在总结一些传统去噪算法的同时指出了去噪算法中几个最新的研究领域;然后提出了几种常见图像噪声的数学统计模型和去噪质量评判标准,接着介绍了两大传统图像去噪算法:中值滤波法和维纳滤波法,对它们的去噪原理和性能进行了详细的讨论与分析。
其次研究了两种最新的图像分析工具:小波变换和多尺度几何变换理论,重点探讨如何将小波变换和Contourlet变换应用于图像去噪,分析了图像经过这两种变换后系数的分布特点以及阈值函数的选取原理,并在此基础上提出了一种基于Contourlet变换的分层阈值去噪算法;并且对以上算法进行了详细的仿真实验,分析了它们的去噪性能。
最后针对原Contourlet变换中的缺陷,提出了一种改进的非采样Contourlet变换:多小波—非采样Contourlet变换:首先利用多小波对图像进行多尺度分解,再结合非下采样方向滤波器组进行方向分解。并将此变换应用于图像去噪之中,并根据分解所得到的各方向子带的关系,改进了Bayes Shrink自适应阈值取值方法,由此提出了一种基于多小波—非采样Contourlet变换的自适应阈值去噪算法。本文对该算法进行仿真实验,且与一些已有的去噪算法进行了对比,实验结果表明:应用此算法的图像去噪效果与传统算法相比,有了一定的提高,能够保留更多的图像细节信息,且具有一定的实用价值。
Digital image noise mainly originates from the process of image acquisition and transmission, which also is one of the main factors influencing the quality of image information. Therefore image de-noising is a popular research subject in image processing area. This paper has researched some crucial techniques and algorisms deeply on this area. The main work and research results will be given as follows:
Firstly this paper provides an overview of development and current situation on image de-noising, and proposes some latest research area, gives some common image statistical mathematical model and the standard of judgment of de-noising quality, then introduces two classical de-noising algorithms :media filter method and wiener filter method, analyses and discusses their de-noising principles and properties emphatically.
Secondly this paper discusses two latest image analysis tools: wavelet transform and Multi-scale Geometry transform, discusses how to apply this two transform on image de-noising, analyses their spreading property of coefficients and threshold choosing principles; on this basic this paper proposes a hierarchical threshold de-noising method based on Contourlet transform, carries on simulation experiment to these algorithm and compares their de-noising results.
Finally according to the drawbacks of Contourlet transform, this paper proposes an improved Contourlet transform: multi wavelet-nonsubsampled Contourlet transform, this algorithm uses multi wavelet for multi-scale decomposing and combines nonsubsampled filter banks for multi-direction decomposing, applies this transform on image de-noising and improves Bayes Shrink Adaptive Threshold method according to the relation between the decomposing sub bands. So this paper proposes a new algorithm which is called multi wavelet-nonsubsampled Contourlet transform de-noising algorithm. The experiment result shows this algorithm is superior to some traditional algorithm that can reserve more image detail information and get a better de-noising effect, which also has certain of application value.
引文
[1] R.C.GanzalenLz,R.E.Wbods.数字图像处理[M].北京:电子工业出版社, 2007.
[2] Pratt.W.K. Digital Image Processing[M]. New York: MIT Press, 2001.
[3] Peebles.P.Z. Probability Random Variables and Random Signal Principles[M]. New York: McGraw-Hill, 1993.
[4] Kenneth R.castleman.数字图象处理[M].北京:电子工业出版社, 2006.
[5]阮秋琦.数字图象处理学[M].北京:电子工业出版社,2004.
[6]陈传波.数字图象处理[M].北京:机械工业出版社,2004.
[7] DONOHO D L. De-noising by soft-thresholding[J]. IEEE Trans on IT, 1995, 41(3):613-627.
[8] SCHULZE M A, JOHN A. Morphological image processing techniques in t-hermo graphic image[J].Biomedical Sciences Instrumentation,1993, 29(2-3):227-234.
[9] SERRA J. Image analysis and mathematical morphology-Volume II[M].NewYork: Academic,1988.
[10]焦李成,谭山.图像的多尺度分析:回顾和展望.电子学报,2003.12 ,31(12A):43-50.
[11]王益艳.图像去噪算法的研究:[陕西师范大学硕士学位论文].西安:陕西师范大学信号与信息处理,2008,1-5.
[12] J.W.Tukey. Exploratory data analysis. Addison-Wesley, Rading,MA,1971.
[13] Gallagher NC, Wise GL.A theoretic analysis of properties of the median fil-ters[J].IEEE Trans. On Acoustics Speech, Signal Processing,1981,29(l):1136-1141.
[14] Brownrigg. The weighted median filter[J].Communication Association Comp-uting Machinery,1984,27(8):807-818.
[15] Ko SJ, Lee SJ. Center Weighted Median Filters and Their Applications to Image Enhancement[J]. IEEE Trans, Circuits Syst,1991, 38(9):984-993.
[16]郭晓新,卢奕南等.自适应定向加权中值滤波[J].吉林大学学报(理学版),2005,43(4):495-499.
[17]刑藏菊,王守觉,邓浩江等.一种基于极值中值的滤波算法[J].中国图象图形学报,2001,6(6):533-536.
[18] Wang JH, Lin LD. An improved median filter using min-max algorithm for image Processing[J]. Electronics Letters,1997,33(16):1360.
[19] G.H.Hwan, R.A.Haddad. Adaptive median filters: new algorithms and results[J]. IEEE Trans on Image Processing,1995,4(4):499-502.
[20] WangZhou, ZhangDavid. Progressive switching median filter for the removal of impulse noise from highly corrupt images[J].IEEE Trans on Circuits and Systems,1999,46(l):78-80.
[21] Adrian BU, Pauli KU. Turning the Smoothness of the Recursive Median Filter[j]. IEEE Trans on Signal Processing,2002,50(7):1631 -1639.
[22] P Ishwar,P Moulin. Multiple-domain image modeling and restoration. In: Proceedings of IEEE international Conference on Image Processing. Kobe Japan,1999,362-366.
[23] Peng-LangShui. Image denoising algorithms via doubly local Wiener filtering with direction windows in wavelet domain[J].IEEE Trans on Signal Processing,2005,12(10):681-684.
[24] Li X, Orchard MT. Spatially adaptive image denoising under over completeexpansion. In: Proceedings of IEEE international Conference on Image Processing. Canada, 2000,300-303.
[25] Mallat S and Hwang W L. Singularity detection and processing with wavelets[J]. IEEE Trans Inform. Theory, 1992, 38(2): 617–643.
[26] Mallat S and Zhong S. Characterization of signal from multiscale edges[J].IEEE Trans. PAMI, 1992, 14(7): 710–732.
[27] Mallat S.信号处理的小波导引.杨力华等译[M].北京:机械工业出版社, 2002.
[28] D.L.Donoho, I.M.Johnstone. Threshold selection for wavelet shrinkage of noisy data[J].IEEE Trans on IT.1994,81(3)425-455.
[29] D.L.Donoho, I.M.Johnstone. Adapting to unknown smoothness via waveletshrinkage[J]. American Statistical Assoc, 1995, 90 (432): 1200–1224.
[30] Zhang XiaoPing, M.D.Desai. Adaptive denoising based on SURE risk[J]. IEEE Sign processing Letters,1985,5(10):265-267.
[31] Gao HY. Wavelet shrinkage denoising using the non-negative garrote[J]. Computational and Graphical Statistics, 1998, 7(4): 469–482.
[32] Gao H, Bruce. A Wave Shrink with firm shrinkage[J]. Statistica Sinica,19-97,7: 855-874.
[33] S G.Chang, B.Yu,M.Verserli. Spatially adaptive wavelet thresholding with context modeling for image denoising[J]. IEEE Trans. Image Processing,2000,9(9):1522-1530.
[34] S.G.Chang, B.Yu, M.Vetterli. Adaptive wavelet thresholding for image denoising and compression[J]. IEEE Trans. Image Processing, 2000,l9:1532-1546.
[35] Xu Y, Weaver J B, Healy D M, et al. Wavelet transform domain filters: aspatially selective noise filtration technique[J].IEEE Trans. Image Processi-ng,1994,3(6): 747–758.
[36] MallatW.L. Hwang. Singularity detection and processing with wavelets[J]. IEEE Trans.on Information Theory,1992,38(2): 617-643.
[37] Ruizhen Zhao,Zhanyi Hu. Denoising algorithm with multiple thresholds based on the relativity exponents of wavelet coefficients, ICSP’06 Proceedings, 2006.11, I:314-317.
[38]侯建华.基于小波及其统计特性的图像去噪方法研究:[华中科技大学博士学位论文].武汉:华中科技大学控制科学与工程,2007,14-35.
[39] E.J.Candes.Ridgelets: Theory and Applications. PH.D.Thesis, Technical Report, Department of statistics, Stanford University.1998.
[40] E.J.Candes: Monoscale redgelets for the representation of images with the edges. Technical Report,Department of Statistic,Stanford University,1999.
[41] E.J.Candes, D.L.Donoho. Curvelets.USA: Department of Statistics,Stanford University,1999.
[42] E.L.Pennec,Mallat. Image compression with geometrical wavelets. Proc.ofICIP2000,2000,661-664.
[43] Do M N, Vetterli M. The contourlet transform: An efficient directional multi-resolution image representation[J].IEEE Trans Image Processing, 2005, 14(12):2091-2106.
[44] Da Cunha A L, Jiangping Zhou, DOM N. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications[J].IEEE Trans Image Processing, 2006, 15(10):3089-3101.
[45] Eslami R, Radha H. Wavelet-based Contourlet transform and its applicationto image coding. In: Proc of International Conference on Image Processing.Piscataway: IEEE Press, 2004: 8554-8556.
[46] COIFMAN R, DONOHO D L. Translation invariant de-noising In: Proc of Lecture Notes in Statistics: Wavelets and Statistics. New York: Springer-Verlag: 1995: 125-150.
[47]练秋生,孔令富.非抽样轮廓波变换构造及其在图像去噪中的应用[J].仪器仪表学报, 2006,27(4): 331-335.
[48]徐华南,刘哲等.Contourlet变换及其在图像去噪中的应用研究[J].2009:26(2),401-405.
[49] Pernoa P. Malik J. Scale-space and edge detection using anisotiop diffusion[J]. IEEE Trans on PAM I, 1990:689-699.
[50] Catte F, Coll T. Image selective smoothing and edge detection by diffusion[J]. IEEE Trans on SIAM J, 1992,29:182-193.
[51] Ghael S, Sayeed A,Baraniuk R. Improved wavelet denoising via empirical wiener filtering. In: Proceedings of SPIE, San Diego, 1999, Vol. 3169: 389–399.
[52] Choi H, Baraniuk R. Analysis of wavelet-domain wiener filters. In: Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1998: 613–616.
[53]李玉峰.小波分析在图像去噪与压缩中应用研究:[中国科学院研究生院博士学位论文].长春:光学机密机械与物理研究所,2006,35-41.
[54] P.J.BurtE,H.Adelson. The Laplacian Pyramid as a compact image[J]. IEEETrans.on Communications,1983,31(4):532-540.
[55] R.H.Bamberge,M.J.T.Smith.A filter bank for the directional decomposition o-f images: Theory and design[J].IEEE Trans.on Signal Processing,1992,40(4):882-891.
[56]易文娟,郁梅,蒋刚毅. Contourlet:一种有效的方向多尺度变换分析方法[J].计算机应用研究, 2006,23(9): 18-22.
[57]董鸿燕,扬卫平,沈振康.基于Contourlet变换的自适应图像去噪方法[J].红外技术, 2006,28(9): 552-556.
[58] Zuo-feng Zhou,Peng-lang Shui. Contourlet-based image denoising algorithmusing directional windows[J].Electronics Letters,2007,43(2):92-93.
[59]余成波.数字图像处理及MATLAB实现[M].重庆:重庆大学出版社,2003.
[60] Goodman T N T, Lee S L .wavelet of multiplicity[J].Trans, Amer. Math Soc. 1994:338. (2), 639-654.
[61] Do M N, Vetterli M. The contourlet transform: an efficient directional multi-resolution image representation[J].IEEE Trans on Image Processing,2005,14(12):2091-2106.
[62] Da Cunha A L.Nonsubsampled contourlet transform toolbox [EB/OL].(2005-11-3),http://www.ifp.uiuc.edu/cunhada/nsct_toolbox..
[2] Pratt.W.K. Digital Image Processing[M]. New York: MIT Press, 2001.
[3] Peebles.P.Z. Probability Random Variables and Random Signal Principles[M]. New York: McGraw-Hill, 1993.
[4] Kenneth R.castleman.数字图象处理[M].北京:电子工业出版社, 2006.
[5]阮秋琦.数字图象处理学[M].北京:电子工业出版社,2004.
[6]陈传波.数字图象处理[M].北京:机械工业出版社,2004.
[7] DONOHO D L. De-noising by soft-thresholding[J]. IEEE Trans on IT, 1995, 41(3):613-627.
[8] SCHULZE M A, JOHN A. Morphological image processing techniques in t-hermo graphic image[J].Biomedical Sciences Instrumentation,1993, 29(2-3):227-234.
[9] SERRA J. Image analysis and mathematical morphology-Volume II[M].NewYork: Academic,1988.
[10]焦李成,谭山.图像的多尺度分析:回顾和展望.电子学报,2003.12 ,31(12A):43-50.
[11]王益艳.图像去噪算法的研究:[陕西师范大学硕士学位论文].西安:陕西师范大学信号与信息处理,2008,1-5.
[12] J.W.Tukey. Exploratory data analysis. Addison-Wesley, Rading,MA,1971.
[13] Gallagher NC, Wise GL.A theoretic analysis of properties of the median fil-ters[J].IEEE Trans. On Acoustics Speech, Signal Processing,1981,29(l):1136-1141.
[14] Brownrigg. The weighted median filter[J].Communication Association Comp-uting Machinery,1984,27(8):807-818.
[15] Ko SJ, Lee SJ. Center Weighted Median Filters and Their Applications to Image Enhancement[J]. IEEE Trans, Circuits Syst,1991, 38(9):984-993.
[16]郭晓新,卢奕南等.自适应定向加权中值滤波[J].吉林大学学报(理学版),2005,43(4):495-499.
[17]刑藏菊,王守觉,邓浩江等.一种基于极值中值的滤波算法[J].中国图象图形学报,2001,6(6):533-536.
[18] Wang JH, Lin LD. An improved median filter using min-max algorithm for image Processing[J]. Electronics Letters,1997,33(16):1360.
[19] G.H.Hwan, R.A.Haddad. Adaptive median filters: new algorithms and results[J]. IEEE Trans on Image Processing,1995,4(4):499-502.
[20] WangZhou, ZhangDavid. Progressive switching median filter for the removal of impulse noise from highly corrupt images[J].IEEE Trans on Circuits and Systems,1999,46(l):78-80.
[21] Adrian BU, Pauli KU. Turning the Smoothness of the Recursive Median Filter[j]. IEEE Trans on Signal Processing,2002,50(7):1631 -1639.
[22] P Ishwar,P Moulin. Multiple-domain image modeling and restoration. In: Proceedings of IEEE international Conference on Image Processing. Kobe Japan,1999,362-366.
[23] Peng-LangShui. Image denoising algorithms via doubly local Wiener filtering with direction windows in wavelet domain[J].IEEE Trans on Signal Processing,2005,12(10):681-684.
[24] Li X, Orchard MT. Spatially adaptive image denoising under over completeexpansion. In: Proceedings of IEEE international Conference on Image Processing. Canada, 2000,300-303.
[25] Mallat S and Hwang W L. Singularity detection and processing with wavelets[J]. IEEE Trans Inform. Theory, 1992, 38(2): 617–643.
[26] Mallat S and Zhong S. Characterization of signal from multiscale edges[J].IEEE Trans. PAMI, 1992, 14(7): 710–732.
[27] Mallat S.信号处理的小波导引.杨力华等译[M].北京:机械工业出版社, 2002.
[28] D.L.Donoho, I.M.Johnstone. Threshold selection for wavelet shrinkage of noisy data[J].IEEE Trans on IT.1994,81(3)425-455.
[29] D.L.Donoho, I.M.Johnstone. Adapting to unknown smoothness via waveletshrinkage[J]. American Statistical Assoc, 1995, 90 (432): 1200–1224.
[30] Zhang XiaoPing, M.D.Desai. Adaptive denoising based on SURE risk[J]. IEEE Sign processing Letters,1985,5(10):265-267.
[31] Gao HY. Wavelet shrinkage denoising using the non-negative garrote[J]. Computational and Graphical Statistics, 1998, 7(4): 469–482.
[32] Gao H, Bruce. A Wave Shrink with firm shrinkage[J]. Statistica Sinica,19-97,7: 855-874.
[33] S G.Chang, B.Yu,M.Verserli. Spatially adaptive wavelet thresholding with context modeling for image denoising[J]. IEEE Trans. Image Processing,2000,9(9):1522-1530.
[34] S.G.Chang, B.Yu, M.Vetterli. Adaptive wavelet thresholding for image denoising and compression[J]. IEEE Trans. Image Processing, 2000,l9:1532-1546.
[35] Xu Y, Weaver J B, Healy D M, et al. Wavelet transform domain filters: aspatially selective noise filtration technique[J].IEEE Trans. Image Processi-ng,1994,3(6): 747–758.
[36] MallatW.L. Hwang. Singularity detection and processing with wavelets[J]. IEEE Trans.on Information Theory,1992,38(2): 617-643.
[37] Ruizhen Zhao,Zhanyi Hu. Denoising algorithm with multiple thresholds based on the relativity exponents of wavelet coefficients, ICSP’06 Proceedings, 2006.11, I:314-317.
[38]侯建华.基于小波及其统计特性的图像去噪方法研究:[华中科技大学博士学位论文].武汉:华中科技大学控制科学与工程,2007,14-35.
[39] E.J.Candes.Ridgelets: Theory and Applications. PH.D.Thesis, Technical Report, Department of statistics, Stanford University.1998.
[40] E.J.Candes: Monoscale redgelets for the representation of images with the edges. Technical Report,Department of Statistic,Stanford University,1999.
[41] E.J.Candes, D.L.Donoho. Curvelets.USA: Department of Statistics,Stanford University,1999.
[42] E.L.Pennec,Mallat. Image compression with geometrical wavelets. Proc.ofICIP2000,2000,661-664.
[43] Do M N, Vetterli M. The contourlet transform: An efficient directional multi-resolution image representation[J].IEEE Trans Image Processing, 2005, 14(12):2091-2106.
[44] Da Cunha A L, Jiangping Zhou, DOM N. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications[J].IEEE Trans Image Processing, 2006, 15(10):3089-3101.
[45] Eslami R, Radha H. Wavelet-based Contourlet transform and its applicationto image coding. In: Proc of International Conference on Image Processing.Piscataway: IEEE Press, 2004: 8554-8556.
[46] COIFMAN R, DONOHO D L. Translation invariant de-noising In: Proc of Lecture Notes in Statistics: Wavelets and Statistics. New York: Springer-Verlag: 1995: 125-150.
[47]练秋生,孔令富.非抽样轮廓波变换构造及其在图像去噪中的应用[J].仪器仪表学报, 2006,27(4): 331-335.
[48]徐华南,刘哲等.Contourlet变换及其在图像去噪中的应用研究[J].2009:26(2),401-405.
[49] Pernoa P. Malik J. Scale-space and edge detection using anisotiop diffusion[J]. IEEE Trans on PAM I, 1990:689-699.
[50] Catte F, Coll T. Image selective smoothing and edge detection by diffusion[J]. IEEE Trans on SIAM J, 1992,29:182-193.
[51] Ghael S, Sayeed A,Baraniuk R. Improved wavelet denoising via empirical wiener filtering. In: Proceedings of SPIE, San Diego, 1999, Vol. 3169: 389–399.
[52] Choi H, Baraniuk R. Analysis of wavelet-domain wiener filters. In: Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1998: 613–616.
[53]李玉峰.小波分析在图像去噪与压缩中应用研究:[中国科学院研究生院博士学位论文].长春:光学机密机械与物理研究所,2006,35-41.
[54] P.J.BurtE,H.Adelson. The Laplacian Pyramid as a compact image[J]. IEEETrans.on Communications,1983,31(4):532-540.
[55] R.H.Bamberge,M.J.T.Smith.A filter bank for the directional decomposition o-f images: Theory and design[J].IEEE Trans.on Signal Processing,1992,40(4):882-891.
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